Conormal bundles with vanishing Maslov form

If M is a Riemannian manifold, and L is a Lagrangian submanifold of T^*M, the Maslov class of L has a canonical representative 1-form which we call the Maslov form of L. We prove that if L =v^*N = conormal bundle of a submanifold N of M, its Maslov form vanishes iff N is a minimal submanifold. Particularly, if M is locally flat v^*N is a minimal Lagrangian submanifold of T^*M iff N is a minimal submanifold of M. This strengthens a result of Harvey and Lawson [H L].